{"id":"https://openalex.org/W4238323774","doi":"https://doi.org/10.1137/0211028","title":"Computation of Matrix Chain Products. Part I","display_name":"Computation of Matrix Chain Products. Part I","publication_year":1982,"publication_date":"1982-05-01","ids":{"openalex":"https://openalex.org/W4238323774","doi":"https://doi.org/10.1137/0211028"},"language":"en","primary_location":{"id":"doi:10.1137/0211028","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0211028","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087577528","display_name":"T. C. Hu","orcid":"https://orcid.org/0009-0005-0844-7506"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"T. C. Hu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042563610","display_name":"Man\u2010Tak Shing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. T. Shing","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087577528"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1538,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.87837838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"362","last_page":"373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7401576638221741},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.7005578279495239},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6623792052268982},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.6165458559989929},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6130155324935913},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.589540958404541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5105057954788208},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4999558925628662},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37591812014579773},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37316638231277466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3716106414794922},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06541988253593445}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7401576638221741},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.7005578279495239},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6623792052268982},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.6165458559989929},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6130155324935913},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.589540958404541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5105057954788208},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4999558925628662},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37591812014579773},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37316638231277466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3716106414794922},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06541988253593445},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0211028","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0211028","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.695.2923","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.695.2923","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ust.hk/mjg_lib/bibs/DPSu/DPSu.Files/0211028.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1655990431","https://openalex.org/W1987507258","https://openalex.org/W2035331304","https://openalex.org/W2041094700","https://openalex.org/W2085140829","https://openalex.org/W3150041682","https://openalex.org/W4254706106"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W2354191502","https://openalex.org/W1972225038","https://openalex.org/W3134658850","https://openalex.org/W2883805925","https://openalex.org/W4200572757","https://openalex.org/W4285148873"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,10,23,29,33,38,50,65],"computation":[4],"of":[5,9,26,40,53,63],"matrix":[6],"chain":[7],"products":[8],"form":[11],"$M_1":[12],"\\times":[13,15,17],"M_2":[14],"\\cdots":[16],"M_{n":[18],"-":[19],"1}":[20],"$.":[21],"If":[22],"matrices":[24],"are":[25],"different":[27],"dimensions,":[28],"order":[30,44,47,62,79],"in":[31,83],"which":[32,48],"product":[34],"is":[35,45],"computed":[36],"affects":[37],"number":[39,52],"operations.":[41,54],"An":[42],"optimum":[43,61,78],"an":[46,60,71,77],"minimizes":[49],"total":[51],"We":[55],"present":[56],"some":[57],"theorems":[58],"about":[59],"computing":[64],"matrices.":[66],"Based":[67],"on":[68],"these":[69],"theorems,":[70],"$O(n\\log":[72],"n)$":[73],"algorithm":[74],"for":[75],"finding":[76],"will":[80],"be":[81],"presented":[82],"Part":[84],"II.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}